The Moderate Resolution Imaging Spectroradiometers (MODIS) aboard the Terra and Aqua platforms have been used to create data products for a range of earth science disciplines, including analyses of the atmospheric aerosol burden. Mid-visible aerosol optical depth (AOD) data products have been generated routinely by a variety of dedicated algorithms over bright (, , ) and dark (, ; ) land surfaces, ocean surfaces (), and as a by-product of algorithms for the atmospheric correction of land/ocean surface reflectance (e.g. ).

The level 2 (L2; orbit-level) MODIS dedicated aerosol data product is known as MOD04 for data generated from MODIS Terra and MYD04 for data from MODIS Aqua (hereafter MXD04 collectively). The latest version of MXD04 products (Collection 6, C6) contains data generated by the Deep Blue (DB) algorithms over land surfaces (), a Dark Target (DT) over-land algorithm, and an over-water algorithm which also uses wavelengths at which the water surface is dark (). These L2 products are generated from level 1b (L1b) calibrated radiance data measured by the MODIS instruments. To decrease noise in the retrieval and provide a manageable data volume, the standard L2 products are provided at a nominal horizontal pixel size of 10 km (referred to as “retrieval pixels”) compared to a L1b pixel size of 0.25–1 km (dependent on band, referred to as “sensor pixels”). As aerosol horizontal variations are often on length scales of the order of tens of kilometres (e.g. ), this pixel size should preserve the underlying spatial shape of aerosol fields without major smoothing of features. Note that a separate nominal 3 km DT product is also available, albeit with larger uncertainties than the 10 km standard product (, ).

However, a consequence of the MODIS scan geometry and Earth's curvature, of which many users of MXD04 data may not be aware, is a distortion of pixel size and shape from the centre to the edge of the swath. This is known as the “bow-tie effect” and has the potential to alias into angle-dependent artefacts and changes in retrieval quality in the derived data sets. It also presents a challenge for the continuation of MODIS-like data sets using similar sensors such as the Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar-orbiting Partnership (S-NPP) platform, launched in late 2011, for which these bow-tie distortions are much smaller. Consequently, data sets generated from similar algorithms may exhibit different angular-dependent characteristics.

The purpose of this study is to illustrate the influence of the MODIS bow-tie distortion on AOD retrievals and examine some techniques for mitigation of these distortions, for potential application in future MODIS (or VIIRS) data reprocessings. Section  discusses MODIS and its scan geometry, providing an illustration of the bow-tie effect and the dependence of MODIS AOD retrievals on view angle. Section  proposes a two-step solution to mitigate these effects, of which the first step is relatively simple and could be accomplished with minor changes to existing MODIS processing algorithms, while the second step would require more careful evaluation. Finally, Sect.  provides a discussion on the importance of the results.

MODIS takes measurements in a total of 36 bands with central wavelengths between 412 nm and 14.4 µm (). The L1b data are organised into 5 min granules, which consist of 1354 pixels across-track and 203 scans along-track. The term “along-track” indicates the direction of the satellite flight track (for daytime data this is approximately from north to south for Terra and from south to north for Aqua, due to the satellites' ∼98.2∘ inclination), while “across-track” indicates the direction perpendicular to the flight track (alternating east–west and west–east for successive scans). This is illustrated in Fig. .

Each scan is approximately 10 km wide at nadir; there are 10 detectors for nominal 1 km bands, 20 detectors for 0.5 km bands, and 40 detectors for the two bands at nominal 0.25 km resolution. Note that these quoted nominal pixel sizes are only approximate, and this terminology is used for simplicity of understanding. and provide more details about MODIS spatial characterisation. The MODIS spatial response functions on a pixel level are not exactly square and have some slight blurring between adjacent pixels. For example, pre-launch characterisation of MODIS Terra revealed band 8 (centred near 412 nm), nominally of 1 km pixel size, had an effective across-track size around 1.08 km across-track and 1.01 km along-track. Distortions are band dependent and, for the bands relevant to AOD retrieval, of similar (fairly small) magnitude. In the present study pixel sizes (lengths) are approximated as half the distance between adjacent pixel centres in each direction. The error introduced by this approximation is much smaller than the distortion of pixel shape/size resulting from the bow-tie effect. Still it is worth bearing in mind that the representation of sensor pixels (and coarser-resolution L2 data) as quadrilaterals is an idealisation. provide some more discussion and on-orbit characterisation of MODIS's spatial performance from the point of view of land surface reflectance data products.

In the L1b products, the data are available both at native resolution and aggregated to the footprints of the coarser bands. For example, MODIS bands 1 and 2, centred near 650 and 860 nm respectively, are recorded with a nominal 0.25 km pixel size; however, they are additionally provided aggregated to the footprints of the 0.5 km bands (which is native resolution for bands 3–7) and 1 km bands (which is native resolution for bands 8–36). DB uses the L1b data aggregated to 1 km while the DT algorithms use the L1b data at 0.5 km.

The L2 aerosol products are created by aggregating blocks of contiguous sensor pixels through one scan along-track and 10 1 km sensor pixels across-track (or 20 0.5 km pixels for the appropriate bands in DT). The DB algorithms () retrieve AOD from suitable (e.g. cloud-free snow-free) data at sensor-pixel resolution and then aggregate to retrieval-pixel resolution (a “retrieve-then-average” technique), while the DT algorithms () average measured reflectance from suitable pixels and then perform a single retrieval at retrieval-pixel resolution (an “average-then-retrieve” technique). The two averaging methods should be equivalent when the underlying scene is homogeneous but not when there is surface or atmospheric heterogeneity. Thus, the L2 aerosol products consist of 135 retrieval-pixel positions across-track and 203 along-track (the four excess across-track nominal 1 km sensor pixels are discarded as 1354 does not divide evenly by 10). As the sensor scans across-track back and forth, the light observed by MODIS is reflected from a scan mirror onto the focal plane assemblies. Dependent on the scan direction, both sides of this scan mirror are used. Differences in the quality of the characterisation of these two mirror sides can lead to striping in the data between forward and reverse scans in some situations ().

Because of this scan geometry the spatial resolution degrades from nadir (viewing zenith angle (VZA) 0∘) to the scan edge (VZA ∼65∘), such that pixels near the edge of the scan are larger than those near nadir; the swath width is ∼2330 km, despite the fact that there are only 1354 across-track sensor pixels. The primary distortion is across-track (i.e. pixels get longer in the longitudinal direction) but there is also an along-track (i.e. latitudinal) distortion, resulting in overlap between pixels from consecutive scans near the swath edges. These give a scan a shape similar to a bow tie, hence the term “bow-tie effect”.

These effects are illustrated for an example MODIS Terra granule in Figs.  and . This granule is the basis for most of the results shown in this study. Note that slight asymmetries and discontinuities in the retrieval-pixel size result because of variations in terrain elevation across the granule. Although the nominal 10km×10 km horizontal resolution results in a retrieval-pixel area of ∼100 km2 near the centre of the swath, as the VZA increases, the pixel area is increased by almost a factor of 10 at the extreme edges of the swath. Figure  shows that the median absolute VZA is about 30∘, for which pixel area is increased by around ∼50 % compared with VZA =0∘. Hence, although the MODIS aerosol retrieval-pixel size is commonly stated to be 10km×10 km, half the time the actual area encompassed by these retrieval pixels is at least 50 % larger than that. Note that the sign of VZA in Fig.  is defined such that positive values are found on the western side of the swath.

Taking a closer view of the area near the western edge of the swath, Fig.  shows the ground locations of the sensor and retrieval pixels. Scans are coloured alternating in red and blue (odd scans in red, even in blue). Two factors are immediately apparent. One is the strong elongation of pixels in the across-track (longitudinal) direction. The second is that, at the swath edge, successive scans (e.g. a red-coloured scan and the blue-coloured scans immediately before and after it) are fully overlapped in the along-track direction. Each edge-of-swath retrieval covers half of the area of the retrieval pixel from the scan before it and half of the area from the scan after it (i.e. they are fully overlapping). Even 10 retrievals in from the scan edge the retrieval pixels are more than half overlapped between successive scans. This therefore represents a sizeable fraction of the MXD04 data, particularly in terms of area covered.

This overlap is not obvious to L2 data product users, as the L2 files only present the central latitudes and longitudes for the retrieval pixels. Figure  shows the same retrieval-pixel locations as in Fig. , except with the retrieval-pixel boundaries which would be inferred from the L2 central latitudes/longitudes overplotted. The fact that the L2 pixels overlap and are oversampled is not clear from the L2 products alone and would require auxiliary knowledge of the L1b sensor-pixel locations, which are not provided in the L2 products.

All other things being equal, the expected effects of both aspects of this distortion (i.e. pixel enlargement and overlap) on the MXD04 products would be to decrease the variability of the retrieved AOD near the edge of the scan compared to that near the centre of the scan. Figure  shows histograms of AOD at 550 nm from all four algorithm/surface types included within the C6 MXD04 products (DB over arid and vegetated surfaces; DT over land and ocean), for data with VZA <10∘ and VZA >55∘, corresponding to roughly the lowest and highest VZA quintiles respectively (Fig. ). These histograms are calculated from all L2 products for the year 2006; for the DT ocean panel only latitudes poleward of 35∘ are used, as otherwise a sampling bias may be introduced due to the presence of sun glint near the centre of the swath in tropical regions.

The median, standard deviations, and width of the central 68 % of the data (i.e. difference between 84th and 16th percentiles of AOD) for these histograms are shown in Table . In all cases, the retrievals near the edge of the swath show smaller variability than those near the centre, which is consistent with the expected effects of the bow-tie distortion. The median AOD is more stable between the two sets of VZA. The decrease in variability (∼25 % decrease in AOD standard deviation or width of central 68 %) is most pronounced for the dark (vegetated) land surfaces in DB and DT. This may reflect the lack of strong aerosol point sources over the open ocean and potentially the spatial scales of aerosol features over desert and ocean surfaces being larger than aerosols over vegetated land.

Note that the differences between DB and DT histogram shapes over dark vegetated surfaces are due in part to algorithmic assumptions; for example, what surface counts as dark vs. bright in the two algorithms, and the fact that DT over land allows retrievals of small negative AOD (down to -0.05) while DB does not. All histogram shapes may also be influenced by the fact that the algorithms' AOD retrieval uncertainties are factors of solar/viewing geometry (e.g. , ); depending on the nature of these uncertainties, they may also be contributing to shifts in the shapes of the AOD distributions. It is difficult to disentangle the relative importance of these oversampling and error reduction to the change in width, particularly since the answers are likely to be algorithm specific. However, Table  and Fig.  support the assertion that the retrieval overlap and size distortion, undesirable from a point of view of homogeneity of data characteristics, may also be influencing the statistics of the retrieved AOD.

The full influence of the MODIS bow-tie effect on the MXD04 aerosol data products has not received wide recognition up to this point. Despite the fact that visualisations of the data make the elongation of L2 pixels fairly obvious, the substantial overlap between them at the edge of the swath, and the effect that this oversampling and enlargement may have on the L2 data and aggregated statistics, has been underappreciated, and many data users may be unaware of it because it cannot be inferred from the L2 data products in isolation.

Although this distortion has not hindered the widespread use of the MXD04 data products for scientific applications, the issue is increasingly relevant now that MODIS-like algorithms are being developed for application to NPP-VIIRS data. The VIIRS sensor makes measurements at similar spectral bands to MODIS, with a similar L1b sensor-pixel size of nominal 0.75 km for moderate-resolution bands (M-bands), and a broader swath (3040 km). VIIRS has a similar across-track scanning pattern to MODIS, although with 16 M-band detectors per scan. However, VIIRS incorporates several design features to reduce the bow-tie distortion (, ). Firstly, the VIIRS on-board native pixel size is actually smaller than the nominal M-band size in the across-track direction. The scan is divided into three regions (in both directions). From nadir out to a scan angle of 31.72∘, three pixels are aggregated across-track to create the M-band L1b data; from 31.72 to 44.86∘ two pixels are aggregated, and from 44.86∘ to the edge of scan no aggregation is performed. Additionally, at the outer two aggregation zones, two and four pixels respectively are deleted from the along-track scan edges (so-called “bow-tie deletion”). The net effect of this is that pixels within each aggregation zone are enlarged in length by at most approximately only a factor of 2 and that overlap between sensor pixels from consecutive scans is in most cases two or fewer detectors, compared to up to 100 % in MODIS. Thus, there are structural reasons that, even if the AOD retrieval algorithms are as close as possible, the characteristics of L2 and L3 data derived from the sensors may differ, which has implications for MODIS/VIIRS data continuity and the generation of multi-sensor long-term climate data records.

It is therefore recommended that future reprocessings of the MODIS aerosol data records consider ways to mitigate the effect of the bow-tie distortion on the spatial structure of the AOD products. In the meantime this study is intended to serve as a point of reference to bring these issues to wider recognition within the data user community. Aggregating sensor pixels by geographical location rather than in along-track scan order is one straightforward step which can be taken to decrease the along-track distortion; however, as discussed, taking the additional step of changing to a variable across-track aggregation has larger implications for algorithm development and QA tests. This is already an issue which algorithm developers are facing to an extent, because with the VIIRS bow-tie deletion the number of valid sensor pixels also changes as a function of VZA through the three M-band aggregation zones.

One important caveat to this recommendation is that a strength of the MODIS data product suite is that multiple L2 products are produced on a common grid (e.g. standard nominal 10 km DB and DT aerosol data) or on a common scaling of this detector-based grid (e.g. some cloud products). This makes it fairly straightforward to, for example, perform direct comparisons between the DB and DT aerosol data sets or to collocate aerosol and cloud data products for other studies. If one product were reaggregated then it would make the most sense for others to also be reaggregated to preserve this common structure. Note, however, that many other MODIS data products are essentially ungridded aside from the underlying scan structure (e.g. some nominal 1 km cloud or ocean colour products) or on a grid defined relative to the Earth rather than the satellite (e.g. some land products), in which case comparisons or synergistic applications would be unaffected by the change to atmospheric product aggregation (since the grids are not the same as the aerosol products anyway). In fact, the L2 grids of the MODIS land products were designed in part to account for some of the scan-related distortions ().

The present study has focused on mid-visible AOD, as this is the primary data product from the DB/DT L2 aerosol algorithms. Other retrieved quantities, such as AOD at other wavelengths or the Ångström exponent, are susceptible to these effects in the same way. The effect on downstream L3 products such as mean AOD in a 1∘ box is likely to be smaller on global average since these products represent an additional level of spatial aggregation anyway. However the increase in effective spatial resolution near the edge of the swath resulting from the variable aggregation technique would lead to a greater number of available L2 retrievals to go into the L3 average, potentially resulting in a more accurate grid-box mean AOD. Additionally, the L3 products contain histograms of retrieved AOD; by decreasing effective pixel size and removing the overlap between pixels, these histograms should also become more accurate representations of the aerosol variability within a grid cell. Indeed, a test application to data over North America reveals changes in L3-like data due to changes in off-nadir retrievals. Changes are, however, likely to be algorithm- and region-specific. Therefore, it seems likely that the benefits of reaggregation would extend to the L3 aerosol data products, even though the most substantial benefit is to the L2 products.

Although presented here in the context of the DB and DT AOD retrieval algorithms, these types of issues will be common to any algorithm which aggregates MODIS data to a coarser resolution or to any other sensor with a similar type of scanning geometry and detector setup. The mitigation is fairly straightforward for this example because the MXD04 spatial resolution matches the along-track length of one scan (i.e. 10 nominal 1 km sensor pixels). However for data products where the L2 resolution does not match the scan length, such as the DT nominal 3 km AOD product (), the distortion will have an irregular impact on the actual and perceived size of the L2 retrieval pixels. Thus, to obtain a L2 product where the pixel-to-pixel variation in area covered is minimised, it makes most sense to perform retrievals at either the coarsest L1b data pixel size (i.e. nominal 1 km for MODIS or 0.75 km for VIIRS) or else with an along-track aggregation which is an exact divisor (or multiple) of the scan length (e.g. 2, 5, or 10  km for MODIS; 3, 6, or 12 km for VIIRS).